The Question:

What dialect are the characters in Guys and
Dolls speaking?

The Answer:

"Runyonese."

Guys and
Dolls, a musical and motion picture, is based on
the book of the same name by Damon Runyon. Runyon was
distinguished for his sports columns and humorous short stories.
Characters in his stories—which took place in New York City's Broadway
area—used a distinctive slang-filled dialect that almost certainly
never existed anywhere other than in his writings. To quote a
1949 review in TIME magazine:

Latter-day Runyon creatures spoke a language of their own, a
dialect which showed traces of remote English ancestry but which,
despite its lack of formal grammar, was curiously courtly in its
rhythms. When a Runyon character wanted to say that a tout had left
money to his girl friend to buy him a tombstone, he said, "I am
under the impression that he leaves Beatrice well loaded as far as
the do-re-mi is concerned and I take it for granted that she handles
the stone situation." In Runyonese there was only one tense, the
universal present, for the characters who used it were usually too
engrossed in the immediate moment to look either backward or
forward.